We use a GEANT4 based [1]} Monte Carlo (MC) simulation to
optimize the event selection
criteria, determine the detection efficiency, and estimate
backgrounds.
In the studies presented here, the \(h_c\)  is
reconstructed via its electric-dipole (E1) transition \(h_c\rightarrow \gamma \eta _c\)  with \(\eta _c\rightarrow X_i\) , where \(X_i\)  denotes 16
hadronic final states: \(p\bar{p}\) , \(\pi ^+\pi ^-K^+K^-\) , \(\pi ^+\pi ^-p\bar{p}\) , \(2(K^+K^-)\) , \(2(\pi ^+\pi ^-)\) ,
\(3(\pi ^+\pi ^-)\) , \(2(\pi ^+\pi ^-)K^+K^-\) , \(K_SK^{\pm }\pi ^{\mp }\) ,
\(K_SK^{\pm }\pi ^{\mp }\pi ^+\pi ^-\) , \(K^+K^-\pi ^0\) , \(K^+K^-\eta \) , \(p\bar{p}\pi ^0\) , \(\pi ^+\pi ^-\eta \) ,
\(\pi ^+\pi ^-\pi ^0\pi ^0\) , \(2(\pi ^+\pi ^-)\eta \) , and \(2(\pi ^+\pi ^-\pi ^0)\) .
The initial state radiation (ISR) is simulated with KKMC [2]},
where the Born cross section of \(e^+e^-\rightarrow \pi ^{0}\pi ^{0}h_{c}\)  is assumed to follow
the \(e^+e^-\rightarrow \pi ^+\pi ^-h_c\)  line-shape [3]}.
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